T9s
63.96%
Wins 63.08%, ties 1.76%
54s
36.04%
Wins 35.16%, ties 1.76%
T9s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| T9s | 63.076 | 1.763 | 35.161 | 63.958 |
| 54s | 35.161 | 1.763 | 63.076 | 36.042 |
This is a contest between two suited hands, T9s and 54s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
T9s is ahead, but 54s is far from dead: it takes 351 of every 1,000 deals outright. Of every 100 boards, about 1.76 are split pots, and the equity figures already include them.
T9s ranks number 64 of 169 starting hands, and 54s ranks number 136, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| T9s | 17,281,000 | 483,000 | 9,633,000 |
| 54s | 9,633,000 | 483,000 | 17,281,000 |
The total is exact: 16 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| T9s | 1.775 | 1.585 | 2.844 | 0.564 |
| 54s | 0.564 | 2.844 | 1.585 | 1.775 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
By flop texture, T9s' equity runs from 52.29% on low rainbow flops (nine high or lower) up to 67.55% on rainbow flops topped by a ten or better. T9s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | T9s wins | Ties | 54s wins | T9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 66.982 | 1.140 | 31.878 | 67.552 |
| Rainbow, nine or lower | 5.689 | 51.992 | 0.589 | 47.419 | 52.287 |
| Two-tone | 46.727 | 63.152 | 0.948 | 35.900 | 63.626 |
| Monotone | 5.273 | 59.228 | 3.968 | 36.804 | 61.212 |
| Paired | 17.091 | 61.982 | 4.621 | 33.397 | 64.292 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Each hand has a baseline against a random hand: 54.03% for T9s, 41.45% for 54s. Here the change is +9.93 and -5.41 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| T9s, all flops | 63.958 | 54.028 | +9.930 | 1.18379 |
| T9s, rainbow, ten or higher | 67.552 | 54.028 | +13.524 | 1.25031 |
| T9s, rainbow, nine or lower | 52.287 | 54.028 | -1.741 | 0.96778 |
| T9s, two-tone | 63.626 | 54.028 | +9.598 | 1.17765 |
| T9s, monotone | 61.212 | 54.028 | +7.184 | 1.13297 |
| T9s, paired | 64.292 | 54.028 | +10.264 | 1.18998 |
| 54s, all flops | 36.042 | 41.453 | -5.411 | 0.86947 |
| 54s, rainbow, ten or higher | 32.448 | 41.453 | -9.005 | 0.78277 |
| 54s, rainbow, nine or lower | 47.713 | 41.453 | +6.260 | 1.15101 |
| 54s, two-tone | 36.374 | 41.453 | -5.079 | 0.87748 |
| 54s, monotone | 38.788 | 41.453 | -2.665 | 0.93571 |
| 54s, paired | 35.708 | 41.453 | -5.745 | 0.86141 |
Does a shared suit matter?
When the hands share a suit, T9s holds 66.38%; when they do not, it holds 63.15%. T9s does better with a shared suit, by 3.23 points.
| Deals | Specific deals | Share of deals | T9s wins | Ties | 54s wins | T9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 65.427 | 1.912 | 32.661 | 66.383 |
| No shared suit | 12 | 75.00 | 62.293 | 1.713 | 35.994 | 63.149 |
How often this matchup comes up
This page stands for 16 specific-card matchups (0.0010% of 1,624,350 ordered deals), or 32 once you count the seats both ways (0.0020%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average T9s takes back $127.92 of it, which is $27.92 more than it put in, and 54s takes back $72.08, $27.92 less than it put in.
Over a long run, 1,000 deals split into about 631 for T9s, 351 for 54s and 18 tied.
The same matchup from the other side
54s against T9s adds nothing new: it is 36.04% for 54s and 63.96% for T9s, the same figures reversed.
Keep exploring
The calculator link fills in Ts9s against 5h4h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of T9s against 54s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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